import {
  Curve,
  Vector3
} from "../../build/three.module.js";

/**
 * A bunch of parametric curves
 *
 * Formulas collected from various sources
 * http://mathworld.wolfram.com/HeartCurve.html
 * http://mathdl.maa.org/images/upload_library/23/stemkoski/knots/page6.html
 * http://en.wikipedia.org/wiki/Viviani%27s_curve
 * http://mathdl.maa.org/images/upload_library/23/stemkoski/knots/page4.html
 * http://www.mi.sanu.ac.rs/vismath/taylorapril2011/Taylor.pdf
 * https://prideout.net/blog/old/blog/index.html@p=44.html
 */

var Curves = (function () {

  // GrannyKnot

  function GrannyKnot() {

    Curve.call(this);

  }

  GrannyKnot.prototype = Object.create(Curve.prototype);
  GrannyKnot.prototype.constructor = GrannyKnot;

  GrannyKnot.prototype.getPoint = function (t, optionalTarget) {

    var point = optionalTarget || new Vector3();

    t = 2 * Math.PI * t;

    var x = -0.22 * Math.cos(t) - 1.28 * Math.sin(t) - 0.44 * Math.cos(3 * t) - 0.78 * Math.sin(3 * t);
    var y = -0.1 * Math.cos(2 * t) - 0.27 * Math.sin(2 * t) + 0.38 * Math.cos(4 * t) + 0.46 * Math.sin(4 * t);
    var z = 0.7 * Math.cos(3 * t) - 0.4 * Math.sin(3 * t);

    return point.set(x, y, z).multiplyScalar(20);

  };

  // HeartCurve

  function HeartCurve(scale) {

    Curve.call(this);

    this.scale = (scale === undefined) ? 5 : scale;

  }

  HeartCurve.prototype = Object.create(Curve.prototype);
  HeartCurve.prototype.constructor = HeartCurve;

  HeartCurve.prototype.getPoint = function (t, optionalTarget) {

    var point = optionalTarget || new Vector3();

    t *= 2 * Math.PI;

    var x = 16 * Math.pow(Math.sin(t), 3);
    var y = 13 * Math.cos(t) - 5 * Math.cos(2 * t) - 2 * Math.cos(3 * t) - Math.cos(4 * t);
    var z = 0;

    return point.set(x, y, z).multiplyScalar(this.scale);

  };

  // Viviani's Curve

  function VivianiCurve(scale) {

    Curve.call(this);

    this.scale = (scale === undefined) ? 70 : scale;

  }

  VivianiCurve.prototype = Object.create(Curve.prototype);
  VivianiCurve.prototype.constructor = VivianiCurve;

  VivianiCurve.prototype.getPoint = function (t, optionalTarget) {

    var point = optionalTarget || new Vector3();

    t = t * 4 * Math.PI; // normalized to 0..1
    var a = this.scale / 2;

    var x = a * (1 + Math.cos(t));
    var y = a * Math.sin(t);
    var z = 2 * a * Math.sin(t / 2);

    return point.set(x, y, z);

  };

  // KnotCurve

  function KnotCurve() {

    Curve.call(this);

  }

  KnotCurve.prototype = Object.create(Curve.prototype);
  KnotCurve.prototype.constructor = KnotCurve;

  KnotCurve.prototype.getPoint = function (t, optionalTarget) {

    var point = optionalTarget || new Vector3();

    t *= 2 * Math.PI;

    var R = 10;
    var s = 50;

    var x = s * Math.sin(t);
    var y = Math.cos(t) * (R + s * Math.cos(t));
    var z = Math.sin(t) * (R + s * Math.cos(t));

    return point.set(x, y, z);

  };

  // HelixCurve

  function HelixCurve() {

    Curve.call(this);

  }

  HelixCurve.prototype = Object.create(Curve.prototype);
  HelixCurve.prototype.constructor = HelixCurve;

  HelixCurve.prototype.getPoint = function (t, optionalTarget) {

    var point = optionalTarget || new Vector3();

    var a = 30; // radius
    var b = 150; // height

    var t2 = 2 * Math.PI * t * b / 30;

    var x = Math.cos(t2) * a;
    var y = Math.sin(t2) * a;
    var z = b * t;

    return point.set(x, y, z);

  };

  // TrefoilKnot

  function TrefoilKnot(scale) {

    Curve.call(this);

    this.scale = (scale === undefined) ? 10 : scale;

  }

  TrefoilKnot.prototype = Object.create(Curve.prototype);
  TrefoilKnot.prototype.constructor = TrefoilKnot;

  TrefoilKnot.prototype.getPoint = function (t, optionalTarget) {

    var point = optionalTarget || new Vector3();

    t *= Math.PI * 2;

    var x = (2 + Math.cos(3 * t)) * Math.cos(2 * t);
    var y = (2 + Math.cos(3 * t)) * Math.sin(2 * t);
    var z = Math.sin(3 * t);

    return point.set(x, y, z).multiplyScalar(this.scale);

  };

  // TorusKnot

  function TorusKnot(scale) {

    Curve.call(this);

    this.scale = (scale === undefined) ? 10 : scale;

  }

  TorusKnot.prototype = Object.create(Curve.prototype);
  TorusKnot.prototype.constructor = TorusKnot;

  TorusKnot.prototype.getPoint = function (t, optionalTarget) {

    var point = optionalTarget || new Vector3();

    var p = 3;
    var q = 4;

    t *= Math.PI * 2;

    var x = (2 + Math.cos(q * t)) * Math.cos(p * t);
    var y = (2 + Math.cos(q * t)) * Math.sin(p * t);
    var z = Math.sin(q * t);

    return point.set(x, y, z).multiplyScalar(this.scale);

  };

  // CinquefoilKnot

  function CinquefoilKnot(scale) {

    Curve.call(this);

    this.scale = (scale === undefined) ? 10 : scale;

  }

  CinquefoilKnot.prototype = Object.create(Curve.prototype);
  CinquefoilKnot.prototype.constructor = CinquefoilKnot;

  CinquefoilKnot.prototype.getPoint = function (t, optionalTarget) {

    var point = optionalTarget || new Vector3();

    var p = 2;
    var q = 5;

    t *= Math.PI * 2;

    var x = (2 + Math.cos(q * t)) * Math.cos(p * t);
    var y = (2 + Math.cos(q * t)) * Math.sin(p * t);
    var z = Math.sin(q * t);

    return point.set(x, y, z).multiplyScalar(this.scale);

  };

  // TrefoilPolynomialKnot

  function TrefoilPolynomialKnot(scale) {

    Curve.call(this);

    this.scale = (scale === undefined) ? 10 : scale;

  }

  TrefoilPolynomialKnot.prototype = Object.create(Curve.prototype);
  TrefoilPolynomialKnot.prototype.constructor = TrefoilPolynomialKnot;

  TrefoilPolynomialKnot.prototype.getPoint = function (t, optionalTarget) {

    var point = optionalTarget || new Vector3();

    t = t * 4 - 2;

    var x = Math.pow(t, 3) - 3 * t;
    var y = Math.pow(t, 4) - 4 * t * t;
    var z = 1 / 5 * Math.pow(t, 5) - 2 * t;

    return point.set(x, y, z).multiplyScalar(this.scale);

  };

  var scaleTo = function (x, y, t) {

    var r = y - x;
    return t * r + x;

  };

  // FigureEightPolynomialKnot

  function FigureEightPolynomialKnot(scale) {

    Curve.call(this);

    this.scale = (scale === undefined) ? 1 : scale;

  }

  FigureEightPolynomialKnot.prototype = Object.create(Curve.prototype);
  FigureEightPolynomialKnot.prototype.constructor = FigureEightPolynomialKnot;

  FigureEightPolynomialKnot.prototype.getPoint = function (t, optionalTarget) {

    var point = optionalTarget || new Vector3();

    t = scaleTo(-4, 4, t);

    var x = 2 / 5 * t * (t * t - 7) * (t * t - 10);
    var y = Math.pow(t, 4) - 13 * t * t;
    var z = 1 / 10 * t * (t * t - 4) * (t * t - 9) * (t * t - 12);

    return point.set(x, y, z).multiplyScalar(this.scale);

  };

  // DecoratedTorusKnot4a

  function DecoratedTorusKnot4a(scale) {

    Curve.call(this);

    this.scale = (scale === undefined) ? 40 : scale;

  }

  DecoratedTorusKnot4a.prototype = Object.create(Curve.prototype);
  DecoratedTorusKnot4a.prototype.constructor = DecoratedTorusKnot4a;

  DecoratedTorusKnot4a.prototype.getPoint = function (t, optionalTarget) {

    var point = optionalTarget || new Vector3();

    t *= Math.PI * 2;

    var x = Math.cos(2 * t) * (1 + 0.6 * (Math.cos(5 * t) + 0.75 * Math.cos(10 * t)));
    var y = Math.sin(2 * t) * (1 + 0.6 * (Math.cos(5 * t) + 0.75 * Math.cos(10 * t)));
    var z = 0.35 * Math.sin(5 * t);

    return point.set(x, y, z).multiplyScalar(this.scale);

  };

  // DecoratedTorusKnot4b

  function DecoratedTorusKnot4b(scale) {

    Curve.call(this);

    this.scale = (scale === undefined) ? 40 : scale;

  }

  DecoratedTorusKnot4b.prototype = Object.create(Curve.prototype);
  DecoratedTorusKnot4b.prototype.constructor = DecoratedTorusKnot4b;

  DecoratedTorusKnot4b.prototype.getPoint = function (t, optionalTarget) {

    var point = optionalTarget || new Vector3();

    var fi = t * Math.PI * 2;

    var x = Math.cos(2 * fi) * (1 + 0.45 * Math.cos(3 * fi) + 0.4 * Math.cos(9 * fi));
    var y = Math.sin(2 * fi) * (1 + 0.45 * Math.cos(3 * fi) + 0.4 * Math.cos(9 * fi));
    var z = 0.2 * Math.sin(9 * fi);

    return point.set(x, y, z).multiplyScalar(this.scale);

  };

  // DecoratedTorusKnot5a

  function DecoratedTorusKnot5a(scale) {

    Curve.call(this);

    this.scale = (scale === undefined) ? 40 : scale;

  }

  DecoratedTorusKnot5a.prototype = Object.create(Curve.prototype);
  DecoratedTorusKnot5a.prototype.constructor = DecoratedTorusKnot5a;

  DecoratedTorusKnot5a.prototype.getPoint = function (t, optionalTarget) {

    var point = optionalTarget || new Vector3();

    var fi = t * Math.PI * 2;

    var x = Math.cos(3 * fi) * (1 + 0.3 * Math.cos(5 * fi) + 0.5 * Math.cos(10 * fi));
    var y = Math.sin(3 * fi) * (1 + 0.3 * Math.cos(5 * fi) + 0.5 * Math.cos(10 * fi));
    var z = 0.2 * Math.sin(20 * fi);

    return point.set(x, y, z).multiplyScalar(this.scale);

  };

  // DecoratedTorusKnot5c

  function DecoratedTorusKnot5c(scale) {

    Curve.call(this);

    this.scale = (scale === undefined) ? 40 : scale;

  }

  DecoratedTorusKnot5c.prototype = Object.create(Curve.prototype);
  DecoratedTorusKnot5c.prototype.constructor = DecoratedTorusKnot5c;

  DecoratedTorusKnot5c.prototype.getPoint = function (t, optionalTarget) {

    var point = optionalTarget || new Vector3();

    var fi = t * Math.PI * 2;

    var x = Math.cos(4 * fi) * (1 + 0.5 * (Math.cos(5 * fi) + 0.4 * Math.cos(20 * fi)));
    var y = Math.sin(4 * fi) * (1 + 0.5 * (Math.cos(5 * fi) + 0.4 * Math.cos(20 * fi)));
    var z = 0.35 * Math.sin(15 * fi);

    return point.set(x, y, z).multiplyScalar(this.scale);

  };

  return {
    GrannyKnot: GrannyKnot,
    HeartCurve: HeartCurve,
    VivianiCurve: VivianiCurve,
    KnotCurve: KnotCurve,
    HelixCurve: HelixCurve,
    TrefoilKnot: TrefoilKnot,
    TorusKnot: TorusKnot,
    CinquefoilKnot: CinquefoilKnot,
    TrefoilPolynomialKnot: TrefoilPolynomialKnot,
    FigureEightPolynomialKnot: FigureEightPolynomialKnot,
    DecoratedTorusKnot4a: DecoratedTorusKnot4a,
    DecoratedTorusKnot4b: DecoratedTorusKnot4b,
    DecoratedTorusKnot5a: DecoratedTorusKnot5a,
    DecoratedTorusKnot5c: DecoratedTorusKnot5c
  };

})();

export {Curves};
